Theorem ex-uni 27413

Description: Example for df-uni 4469. Example by David A. Wheeler. (Contributed by Mario Carneiro, 2-Jul-2016.)

Assertion

Ref	Expression
ex-uni	⊢ ∪ {{1, 3}, {1, 8}} = {1, 3, 8}

Proof of Theorem ex-uni

Step	Hyp	Ref	Expression
1		prex 4939	. . 3 ⊢ {1, 3} ∈ V
2		prex 4939	. . 3 ⊢ {1, 8} ∈ V
3	1, 2	unipr 4481	. 2 ⊢ ∪ {{1, 3}, {1, 8}} = ({1, 3} ∪ {1, 8})
4		ex-un 27411	. 2 ⊢ ({1, 3} ∪ {1, 8}) = {1, 3, 8}
5	3, 4	eqtri 2673	1 ⊢ ∪ {{1, 3}, {1, 8}} = {1, 3, 8}

Syntax hints:   = wceq 1523   ∪ cun 3605  {cpr 4212  {ctp 4214  ∪ cuni 4468  1c1 9975  3c3 11109  8c8 11114

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1762  ax-4 1777  ax-5 1879  ax-6 1945  ax-7 1981  ax-9 2039  ax-10 2059  ax-11 2074  ax-12 2087  ax-13 2282  ax-ext 2631  ax-sep 4814  ax-nul 4822  ax-pr 4936

This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-tru 1526  df-ex 1745  df-nf 1750  df-sb 1938  df-clab 2638  df-cleq 2644  df-clel 2647  df-nfc 2782  df-v 3233  df-dif 3610  df-un 3612  df-in 3614  df-ss 3621  df-nul 3949  df-sn 4211  df-pr 4213  df-tp 4215  df-uni 4469

This theorem is referenced by: (None)